A 6m deal is on the table and Chelsea will snap Everton's hand off to grab it.
With Jose Mourinho set to sign another midfielder this summer, offloading Parker a £10m signing from Charlton Athletic in 16 months ago, is seen as good business by the Chelsea management.
Parker did not enjoy his time at the Bridge, playing only 28 times for the Blues and sustaining persistent foot injuries.
But if his medical goes through okay, Parker will sign subject to personal terms being met.